Concept explainers
To compute: The present value of
It refers to the ability of the currency to buy something. Purchasing power decreases with increase in inflation and increase with decrease in inflation.
Explanation of Solution
Given,
Semi annual payments are of $6,175.
Discount rate is 11%.
Semiannual rate is 5.054%.
Formula to calculate present value of annuity,
Where,
- PVA is present value of annuity.
Substitute $6,175 for semiannual payment, and 5.054% for semi annual rate,
Hence, the present value of annuity is $46,592.84.
Effective annual rate is 11.48%.
Given, number of years is 4.
Formula to calculate present value of annuity for 5 years,
Where,
- PVA means present value of annuity.
Substitute $46,592.84 for total PVA, 5.5% for effective annual rate and 4 for number of years.
Hence, the present value of annuity of 5 years is $37,610.52.
Compute present value of annuity for 3 years.
Number of years that will be taken is 6.
Formula to calculate present value of annuity for 3 years,
Where,
- PVA means present value of annuity.
Substitute $46,592.84 for total PVA, 5.5% for effective annual rate and 6 for number of years.
Hence, the present value of annuity of 3 years is $33,791.26.
Compute present value of annuity for current year.
Number of years that will be taken is 9.
Formula to calculate present value of annuity for current year,
Where,
- PVA is present value of annuity.
Substitute $47,154.54 for total PVA, 5.5% for effective annual rate and 9 for number of years.
Hence, the present value of annuity of 3 years is $28,778.78.
Working Note:
Computation of monthly rate,
Hence, the monthly rate is 0.0091.
Computation of semi annual rate,
Hence, the semiannual rate is 5.5%.
Computation of early annual rate,
Hence, the effective annual rate is 11.48%.
Hence, the present value annuity for 5 years, 3 years and currently is $37,610.52, $33,791.26 and $28,778.78.
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Chapter 4 Solutions
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